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Rotational Symmetry (AQA GCSE Maths): Revision Note

Exam code: 8300

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on

AQA Maths: FoundationWJEC Eduqas Maths: FoundationWJEC Eduqas Maths: HigherOCR Maths: FoundationOCR Maths: HigherAQA Maths: HigherEdexcel Maths: FoundationEdexcel Maths: Higher

Rotational symmetry

What is the order of rotational symmetry?

  • Rotational symmetry refers to the number of times a shape looks the same as it is rotated 360° about its centre

  • This number is called the order of rotational symmetry

  • Tracing paper can help work out the order of rotational symmetry

    • Draw an arrow on the tracing paper so you can easily tell when you have turned it through 360°

finding the order of rotational symmetry using tracing paper
finding the order of rotational symmetry using tracing paper 2
finding the order of rotational symmetry using tracing paper 3

  • Notice that returning to the original shape contributes 1 to the order

    • This means a shape can never have order 0

    • A shape with rotational symmetry order 1 may be described as not having any rotational symmetry

    • The only time it looks the same is when you get back to the start

Examiner Tips and Tricks

Remember to use the trick above; using an upwards arrow on the tracing paper to show the starting orientation of the shape.

Worked Example

For the shape below, shade exactly 4 more squares so that the shape has rotational symmetry of order 4.

3-1-line-and-rotation-symmetry-we

The shape below appears the same 4 times if rotated through 360 degrees

3-1-1-rotation-symmetry-we-answer

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.